A typical arch with two pinned supports has four unknown reaction components (two at each pin). The three standard equations of equilibrium ($\Sigma F_x = 0$, $\Sigma F_y = 0$, $\Sigma M = 0$) are insufficient to solve for four unknowns, making a two-hinged arch statically indeterminate to the first degree. By introducing a third hinge (usually at the crown), an additional condition equation is created: the internal bending moment at the hinge is zero ($\Sigma M_{\text{hinge}} = 0$). This provides the necessary fourth equation, rendering the entire structure statically determinate and solvable using only the principles of statics.

Because arches push outwards, their supports must be able to resist significant horizontal thrust. This often requires massive, expensive foundation abutments. A common engineering solution is the Tied Arch.

To find the internal normal force ($N$), shear force ($V$), and bending moment ($M$) at a specific point in the arch: